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SUMMARY:Topological Non-Abelian Gauge Structures in Cayley–Schreier Latt
 ices - Tomáš Bzdušek (Zurich)
DTSTART:20251124T140000Z
DTEND:20251124T153000Z
UID:TALK240073@talks.cam.ac.uk
CONTACT:Bo Peng
DESCRIPTION:Topological band theory was recently extended to crystals host
 ing synthetic Z2 fluxes within unit cells\, with the possible symmetry-com
 patible flux arrangements classified by second group cohomology for all tw
 o-dimensional space groups [1]. Notably\, the fluxes enforce the space gro
 up to be projectively represented\, enabling new topological band features
 \, such as Möbius insulators or Klein-bottle Brillouin zones [2]. However
 \, such analyses have not been extended to crystals hosting non-Abelian ga
 uge fields.\n\nSeparately\, noncommutativity of translations has been intr
 oduced to crystalline structures through a construction dubbed Cayley-Schr
 eier lattice [3]. The noncommutativity is achieved by decorating each site
  of a Bravais lattice with a collection of orbitals: one for each element 
 of a discrete group G\, which acts as a gauge group. However\, this resear
 ch has similarly focused on the Abelian choices G = ZN\, leaving non-Abeli
 an generalizations unexplored.\n\nIn this talk\, we first review the notio
 ns of synthetic gauge structures and Cayley–Schreier lattices\, and then
  present our generalization of the Cayley–Schreier construction to non-A
 belian gauge groups [4]. Specifically\, choosing G as the quaternion group
  Q8 = {±1\, ±i\, ±j\, ±k} (which serves as a discretized proxy for SU(
 2) and where i\, j\, k are pairwise anticommuting elements) allows us to s
 imulate known spinful topological insulators in one and two spatial dimens
 ions. The presented construction can be conveniently realized in synthetic
  platforms using only real hopping amplitudes between the orbitals. Our wo
 rk sets the stage to investigate topological band theory in the presence o
 f non-Abelian gauge fields.\n\n\n\n*References:*\n\n[1] Z. Y. Chen\, Z. Zh
 ang\, S. A. Yang\, and Y. X. Zhao\, _Classification of time-reversal-invar
 iant crystals with gauge structures_\, Nat. Commun. *14*\, 743 (2023).\n\n
 [2] T. Li\, J. Du\, Q. Zhang\, Y. Li\, X. Fan\, F. Zhang\, and C. Qiu\, _A
 coustic Möbius Insulators from Projective Symmetry_\, Phys. Rev. Lett. *1
 28*\, 116803 (2022)\;     Z. Y. Chen\, S. A. Yang\, and Y. X. Zhao\, _Bril
 louin Klein bottle from artificial gauge fields_\, Nat. Commun. *13*\, 221
 5 (2022).\n\n[3] M. Marciani\, _Translation Groups for arbitrary Gauge Fie
 lds in Synthetic Crystals with real hopping amplitudes_\, arXiv:2508.08461
  (2025).\n\n[4] Z. Guba\, R.-J. Slager\, L. K. Upreti\, and T. Bzdušek\, 
 _Topological non-Abelian Gauge Structures in Cayley-Schreier Lattices_\, a
 rXiv: 2509.25316 (2025).
LOCATION:Seminar Room 3\, RDC
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